I'm looking at the following differential equation (see Appendix B of the following paper):
$$ \partial_t\mu[V_E]=-\mu[V_E] + C_{EE}[x\nu_E+(1-x)v_{ext}]-C_{EI}J_{EI}\nu_I, $$
where $\mu[V_E]$ is the mean of $V_E$.
This equation is described as "the evolution of the moment $\mu[V_E]$."
My question is, how exactly should I interpret this? Is it simply the derivative of $\mu[V_E]$ with respect to $t$? But $\partial$ is the symbol for a partial derivative. So should I evaluate this differently than I would $d_t\mu[V_E]$ (assuming the latter is something that even makes sense)? What are some strategies I might use to solve this equation?
Some things to note: In this equation, $C_{EE}, x, C_{EI}, J_{EI},$ and $\nu_{ext}$ are constants. $\nu_E$ and $\nu_I$ (I think?) are variables.
I can provide more content-specific information on request. My main concern is getting clear on the notation.
EDIT: I'm not sure whether this is helpful or not, but earlier in the paper, the following definition is given:
$$ \mu_E=C_{EE}J_{EE}[x\nu_E\tau_E+(1-x)\nu_{ext}\tau_E]-C_{EI}J_{EI}\nu_I\tau_E. $$
I say it might not be helpful only because I'm not quite sure whether $\mu_E$ is the same thing as $\mu[V_E]$ (though they're definitely related). Note that the differential equation above is very similar to this equation -- but with, e.g., $J_{EE}$ and $\tau_E$ removed.